It was REALLY tight soldering, and I don’t claim to have done it well. In retrospect, I should have probably tinned the contact points on the PCB before I started, but the space was so tiny that I didn’t think I could.

Anyway, now both arcade controllers have PS1 DualShock controllers for their internal circuit boards, and both work perfectly well with the PC games (PSX->USB Radio Shack converter) and the Xbox (Dreambox PSX->Xbox converter from LikSang.com).